In known mechanisms of this type a member which brings about the transfer of the wires out of the loose bundle engages the wires from beneath. The member may have for example, the form of a threaded spindle cooperating with a wiper (see Austrian patent specification No. 334,717) or the form of a paddlewheel cooperating with guideways (see Austrian patent specification No. 334,168). These known mechanisms are relatively costly, require exact setting of the mechanism to the wire diameter and under unfavourable working conditions, such as particularly when the wires in the bundle are bent, are not adequately reliable in operation.